Problem: Which of the following numbers is a multiple of 6? ${63,73,90,106,115}$
The multiples of $6$ are $6$ $12$ $18$ $24$ ..... In general, any number that leaves no remainder when divided by $6$ is considered a multiple of $6$ We can start by dividing each of our answer choices by $6$ $63 \div 6 = 10\text{ R }3$ $73 \div 6 = 12\text{ R }1$ $90 \div 6 = 15$ $106 \div 6 = 17\text{ R }4$ $115 \div 6 = 19\text{ R }1$ The only answer choice that leaves no remainder after the division is $90$ $ 15$ $6$ $90$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $6$ are contained within the prime factors of $90$ $90 = 2\times3\times3\times5 6 = 2\times3$ Therefore the only multiple of $6$ out of our choices is $90$. We can say that $90$ is divisible by $6$.